Question

One grain of sand approximately weighs 7 * 10^{-5} g. How many grains of sand are there in 6300 kg of sand? Give your answer in standard form.

Answer 1

Answer:

Proportion states that the two ratio or fractions are equal.

Given the statement: One grain of sand approximately weighs 7 * 10^{-5} g.

To find how many grains of sand are there in 6300 kg of sand.

Let x be the number of grains of sand in 6300 kg of sand.

Using conversion :

1 kg = 1000 g

6300 kg = 6300000 g

Then, by using proportion method, we have;

$\frac{1}{7\times 10^{-5}}= \frac{x}{6300000}$

$\frac{10^5}{7} = \frac{x}{6300000}$

By cross multiply we get;

$6300000 \times 10^5 = 7x$

or

$63 \times 10^5 \times 10^5 = 7x$

$63 \times 10^{5+5} = 7x$  [using $x^a \cdot x^b = x^{a+b}$]

$63 \times 10^{10} = 7x$

Divide both sides by 7 we get;

$x = \frac{63 \times 10^{10}}{7} = 9 \times 10^{10}$

Standard form is a way of of writing down very large or very small numbers easily.

Therefore, $9 \times 10^{10}$ grains of sand are there in 6300 kg of sand.